"In his public life, Steve was known as a visionary; in his private life, he cherished his family," they said, requesting privacy and thanking those who had "shared their wishes and prayers" during his final year.

Apple said the company had "lost a visionary and creative genius, and the world has lost an amazing human being".

Tim Cook, who was made Apple's CEO after Mr Jobs stood down in August, said his predecessor had left behind "a company that only he could have built, and his spirit will forever be the foundation of Apple".

Flags are being flown at half mast outside the Apple headquarters in Cupertino, California, while fans of the company have left tributes outside Apple shops around the world.

"What he's done for us as a culture, it resonates uniquely in every person," said Cory Moll, an Apple employee in San Francisco.

"Even if they never use an Apple product, the impact they have had is so far-reaching."

At the company's Shanghai shop, customer Jin Yi said Mr Jobs had created gadgets which had "changed people's perceptions of machines".

Rivals' tributes

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Media captionApple co-founder Steve Wozniak will remember Mr Jobs for "knowing what made sense in a product"

The heads of other leading technology companies have also paid tribute, including Microsoft boss Bill Gates, who said Mr Jobs's "profound impact" on the world of technology would "be felt for many generations to come".

"For those of us lucky enough to get to work with him, it's been an insanely great honour. I will miss Steve immensely."

Facebook founder Mark Zuckerberg thanks Mr Jobs for "showing that what you build can change the world" while Sony Corp president and CEO Howard Stringer said: "The digital age has lost its leading light."

South Korea's Samsung, which is involved in an ongoing legal battle with Apple over patents, praised Mr Jobs for his "numerous revolutionary changes to the information technology industry".

At the scene

By Tom BurridgeBBC News, Apple HQ, Cupertino, California

On the pavements outside the main Apple offices is a small, simple but very effective memorial to Steve Jobs - just like many of the products he designed.

"Jobs" - spelt out in small tea light candles alongside the Chinese symbol for Steve - and then the Apple logo. And inside the candlelit design, an iPad with Steve Jobs's photo on the screen.

Late into the night in America's Silicon Valley they are still arriving to take photos, lay candles and messages. One former employee described Steve Jobs as the John Lennon of technology. Another Taiwanese-born resident of Cupertino who has never bought an Apple product said he came down to pay respects to a man who changed the world.

"His innovative spirit and remarkable accomplishments will forever be remembered by people around the world," said chief executive officer Choi Gee-Sung.

Mr Jobs built a reputation as a forthright and demanding leader who could take niche technologies - such as the mouse and graphical user interface, using onscreen icons rather than text - and make them popular with the general public.

He introduced the colourful iMac computer, the iPod, the iPhone and the iPad to the world. His death came just a day after Apple unveiled its latest iPhone 4S model.

With a market value estimated at $351bn (£227bn), Apple became the world's most valuable technology company.

'Face of Apple'

More than almost any other business leader, Mr Jobs was indistinguishable from his company, which he co-founded in the 1970s.

Life of Steve Jobs

Born in San Francisco in Feb 1955 to students Joanne Schieble and Syrian-born Abdulfattah Jandali - adopted by a Californian working class couple

Had a summer job at Hewlett-Packard while at school - later worked at Atari

Dropped out of college after six months and went travelling in India, where he became a Buddhist

Launched Apple with school friend Steve Wozniak in 1976 - first Apple computer sold the same year

Left Apple amid disputes in 1985 but returned in 1996 and became CEO in 1997

Bought Pixar animation company in 1986 for $10m

Married in a Buddhist ceremony in 1991 - has three children with his wife and a daughter from a previous relationship

Had a personal wealth estimated at $8.3bn (£5.4bn) in 2010

Diagnosed with pancreatic cancer in 2003, and after three periods of sickness leave, resigns as Apple CEO in August 2011